On the Cauchy problem in linear viscoelasticity

Pasquale Renno

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1983)

  • Volume: 75, Issue: 5, page 195-204
  • ISSN: 1120-6330

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Renno, Pasquale. "On the Cauchy problem in linear viscoelasticity." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 75.5 (1983): 195-204. <http://eudml.org/doc/287222>.

@article{Renno1983,
author = {Renno, Pasquale},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {fundamental solution of integro-differential operator equation; tempered distribution associated with a never negative function; explicit solution of Cauchy problem; fading memory; Laplace integral; isotropic, intrinsically homogeneous body; linearly viscoelastic behaviour of creep type; translation invariant axiom; creep representation of linear one- dimensional motions},
language = {eng},
month = {11},
number = {5},
pages = {195-204},
publisher = {Accademia Nazionale dei Lincei},
title = {On the Cauchy problem in linear viscoelasticity},
url = {http://eudml.org/doc/287222},
volume = {75},
year = {1983},
}

TY - JOUR
AU - Renno, Pasquale
TI - On the Cauchy problem in linear viscoelasticity
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1983/11//
PB - Accademia Nazionale dei Lincei
VL - 75
IS - 5
SP - 195
EP - 204
LA - eng
KW - fundamental solution of integro-differential operator equation; tempered distribution associated with a never negative function; explicit solution of Cauchy problem; fading memory; Laplace integral; isotropic, intrinsically homogeneous body; linearly viscoelastic behaviour of creep type; translation invariant axiom; creep representation of linear one- dimensional motions
UR - http://eudml.org/doc/287222
ER -

References

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  2. Coleman, B.D. and Noll, W. (1961) - Foundation of linear viscoelasticity, «Rev. of Modern Physics», 33, 239-249. Zbl0103.40804MR158605
  3. Graffi, D. (1963) - Sulla propagazione nei mezzi dispersivi, «Ann. di Matem. pura e applicata», Serie IV, Tomo LX, 173-194. MR155549
  4. Benvenuti, P. (1965) - Sulla teoria ereditaria delle deformazioni lineari dinamiche, «Rendiconti di Matematica», 255-290. Zbl0158.21501MR205538
  5. Barberan, J. and Herrera, I. (1966) - Uniqueness theorems and speed of propagation of signals in viscoelastic materials, «Arch. Rat. Mech. Anal.», 23 , 173-190. Zbl0151.37401MR221807
  6. Barberan, J. and Herrera, I. (1967) - Riemann representation method in viscoelasticity. II: Cauchy's initial value problem, «Arch. Rat. Mech. Anal.», 25, 178—187. Zbl0189.26702MR210356
  7. Fabrizio, M. (1968) - Sull'equazione di propagazione nei mezzi viscoelastici, «Rend. Ist. Lombardo», A 102, 437-441. Zbl0188.58601
  8. Dafermos, C.M. (1970) - Asymptotic stability in Viscoelasticity, «Arch. Rat. Mech. Anal.», 37 , 297-308. Zbl0214.24503MR281400
  9. Christensen, R.M. (1971) - Theory of Viscoelasticity, Academic Press, New York and London. 
  10. Leitman, M.J. and Fisher, G.M.C. (1973) - The linear theory of Viscoelasticity, «Handbuch der Physik», Band VI a/3, 1-123. 
  11. Fichera, G. (1977) - Analytical problems of hereditary phenomena in materials with memory, Corso C.I.M.E., Bressanone VI-2-11, Liguori (Napoli), 111-169. 
  12. Graffi, D. (1980) - Mathematical models and waves in linear viscoelasticity, Euromech Colloquium 127 on Wave propagation in viscoelastic media, «Pitman Adv. Publ. Comp.», «Research Notes in Mathematics», 52, 1-27. MR580946
  13. Graffi, D. (1983) - On the fading memory, «Applicable Analysis», 15. Zbl0497.73041MR710196DOI10.1080/00036818308839452
  14. Erdelyi, A., Magnus, N., Oberhettinger, F. and Tricomi, F.G. (1954) - Tables of integral transforms, Vol. I, McGraw-HillBook Comp.. Zbl0055.36401
  15. D'Acunto, B., D'Anna, A. and Renno, P. (1983) - On the motion of a viscoelastic solid in presence of a rigid wall, Part I, «ZAMP», 34 (4), 421-438. MR718848DOI10.1007/BF00944706
  16. Renno, P. (1983) - On a wave theory for the operator ϵ ⁢ ∂ t ⁡ ( ∂ t 2 - c 1 2 ⁢ Δ ) + ∂ t 2 - c 0 2 ⁢ Δ , to be published on «Annali di Matematica Pura e Applicata». 

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